In general, the positioning system of an aircraft (while on the ground and in flight) is based in particular on a satellite positioning system, specifically a GPS type system (“Global Positioning System” in English).
In this case, the message is superimposed on a code that contains the time reference. The synchronization of signals is obtained through atomic clocks on board of each satellite. The receiver compares the shift between the received signal and the locally generated signal in the receiver and measures in this way the distance of the corresponding satellite. These measurements are repeated for all satellites, from which signals are received and used to continuously calculate the position.
Regardless of the system used (low or geostationary constellation or local beacon), each distance measurement places the receiver on a sphere centered on the transmitter. By using at least three transmitters, these spheres have a single intersection point. However, this simple principle becomes complicated because:                the local clock of the receiver is rarely of atomic precision: only the time differences are accurate, which requires four beacons or satellites instead of three to determine a point (if the altitude is known, three beacons are sufficient);        the receivers are mobile, and the measurements are carried out at different points, and        the speed of radio waves varies slightly depending on the traversed ionospheric layers.        
Therefore, the receiver integrates these various errors, using corrections and measurements of various satellites or beacons, followed by integration techniques such as filtering with Kalman filters to obtain the most probable point and its estimated accuracy, speed and universal time.
For applications requiring absolute safety of the point (landing without visibility, anti-collision, . . . ), the navigation signals are supplemented by a so-called “integrity” signal that eliminates any measurement coming from a transmitter that is temporarily or long term out of order. The integrity is a measure of the confidence that the user has in the quality of the system outputs.
Today, position calculation means are used based on hybridizations between GPS data and aircraft inertial data. The hybridization consists in cushioning or stabilizing divergent errors of an inertial navigation station thanks to a position measurement resulting from GPS data. In the Kalman filter, the GPS data is used to estimate the positioning error of IRS type inertial systems (“Inertial Reference System” in English) and to estimate the position in more accurate manner.
In some solutions, there is a main filter which provides one main GPIRS point estimated using N possible satellites and N−1 secondary filters each using a subset of satellites. The bank of Kalman sub-filters performs a detection and exclusion function of a FDE type satellite failure (“Fault Detection and Exclusion” in English).
For ground navigation, the emphasis is on accuracy and in general banks of sub-filters are not employed. The estimated position is therefore a GPIRS position calculated with all known errors or a position with guaranteed accuracy of 95%.
This position can often be completed by retiming of the augmented GPS points in order to improve the GPS guaranteed precision to 95%. The goal of the GPIRS calculated on the ground is not to degrade in any case the accuracy provided by the GPS, but to provide continuity in the event of GPS signal masking or non-availability of GPS signals.
In contrast, the main filter and the N−1 secondary filters are used for the flight. The recognized confidence factor is estimated at 10−7, which means that the probability of the estimated GPIRS point being outside an integrity protection radius is smaller than 10−7.
The confidence level is estimated by assuming that the GPIRS position calculated by an electronic entity has a confidence level of only 10−5, or a factor of ten relative to the error probability of an electronic entity, or 10−6. It is then assumed that the GPIRS data supplied by a number of N redundancies raises the confidence factor from 10−5 to 10−7 through consolidation of the calculated data and exclusion of erroneous data if the number of redundancies is sufficient (minimum 3 for exclusion).
Moreover, we know that the positioning system of an aircraft using a satellite positioning system, specifically a GPS type, as mentioned above, is subject on the ground to so-called multipath phenomena that disrupt the accuracy of the position measurement, so that the obtained GPS position is no longer accurate enough, or a hybrid position calculated starting from such a GPS position has insufficient integrity, to allow its use on the ground.
Indeed, when the signal emitted by a satellite encounters an obstacle, currents are generated on the obstacle, which emits radiation in return. This principle is called electromagnetic diffraction. According to this definition, the term diffraction includes all interaction phenomena such as reflection, diffraction by edges, transmission and masking for instance. In the context of positioning through GPS data, electromagnetic fields diffracted by obstacles in the vicinity of the receiver antenna, such as for instance buildings, are transformed into echo signals called multipath signals. In the presence of such multipath signals, the estimation of the propagation delay between the satellite and the receiver may be degraded and the resulting position may be less accurate.
Furthermore, it is known that some recent functions require aircraft to provide also on the ground an integrity position to ensure quick turns after landing or to navigate in complex airports with a level of confidence in the position. Because of the multipath problems presented above, a position or confidence in the position of the aircraft cannot be guaranteed, because the signals are no longer guaranteed.